OrcaFlex Manual - Orcina

Theory, Environment Theory
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Another way of looking at the problem is in terms of energy. The total energy required to accelerate a body in a
stationary fluid is the sum of the kinetic energy of the body itself, and the kinetic energy of the flow field about the
body. These energies correspond to the terms (m.a) and Ca.Δ.a respectively.
Trapped Water
The term (Ca.Δ) has the dimensions of mass and has become known as the added mass. This is an unfortunate name
which has caused much confusion over the years. It should not be viewed as a body of fluid trapped by and moving
with the body. Some bodies are so shaped that this does occur, but this trapped water is a completely different
matter. Trapped water occurs when the body contains a closed flooded space, or where a space is sufficiently closely
surrounded to prevent free flow in and out. Trapped water should be treated as part of the body: the mass of the
trapped water should be included in the body mass, and its volume should be included in the body volume.
For a more complete description of Morison's equation and a detailed derivation of the added mass component see
Barltrop and Adams, 1991 and Faltinsen, 1990.
5.10.6 Waves
Wave Theory
Each wave train can be a regular wave, a random wave or specified by a time history file.
Regular Waves
OrcaFlex offers a choice of a long-crested, regular, linear Airy wave (including seabed influence on wave length) or
non-linear waves using Dean, Stokes' 5th or Cnoidal wave theories (see Non-linear Wave Theories). Waves are
specified in terms of height and period, and direction of propagation.
Random Waves
OrcaFlex offers five standard frequency spectra: JONSWAP, ISSC (also known as Bretschneider or modified Pierson-
Moskowitz), Ochi-Hubble, Torsethaugen and Gaussian Swell.
The program synthesises a wave time history from a user-determined number of linear wave components. The
wave component frequencies are chosen using an equal energy approach – see below. The phases associated with
each wave component are pseudo-random: a random number generator is used to assign phases, but the sequence
is repeatable, so the same user data will always give the same train of waves. Different wave component phasing for
the same spectrum can be obtained by shifting the simulation time origin relative to the wave time origin, or by
specifying a different random number seed.
OrcaFlex provides special facilities to assist in selecting an appropriate section of random sea. These are available on
the Waves Preview page of the Environment data form. The facilities include:
� A profile graph plotting the wave elevation for a selected period and
� A table listing all the waves in a selected time interval whose height or steepness is large by comparison with
the reference wave Hs, Tz.
Wave components
An irregular wave train is constructed by linear superposition of a number of linear wave components. OrcaFlex
creates the components using an equal area approach, over a user-specified range of the frequency spectrum.
However this approach can result in some components (e.g. near the tails of the spectrum where the spectral energy
is low) representing a wide range of frequencies. Such components can result in poor modelling of system
responses, since a wide frequency range of spectral energy is then concentrated at a single frequency. To solve this
the user can specify a maximum component frequency range, and any component that covers a wider frequency
range is then subdivided into multiple components (which then have lower energy, so they are no longer have equal
energy) until all the components satisfy the specified maximum frequency range.
This method of allocating wave components is now described in more detail. We denote by rmin and rmax the
minimum and maximum relative frequencies, and by δfmax the maximum component frequency range.
The wave components are created as follows:
1. We define fm- to be the frequency of the spectral peak with the lowest frequency. Likewise define fm+ to be the
frequency of the spectral peak with the highest frequency. For single peaked spectra fm- = fm+ = fm. For the Ochi-
Hubble spectrum, the spectral peak frequencies are data items named fm1 and fm2. For the Torsethaugen